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XRD analysis determined crystal cage occupying number n of carbon anion substituted mayenite-type cage compound C12A7: nC

  • Cong Ji EMAIL logo and Fan Gu
Published/Copyright: June 26, 2023
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Science and Engineering of Composite Materials
From the journal Science and Engineering of Composite Materials Volume 30 Issue 1

Abstract

In this study, a series of samples of C12A7 derivative was prepared by high temperature sintering in a sealed graphite crucible. The theoretical model of C12A7 derivatives with different carbon occupation numbers was established. The X-ray diffraction (XRD) theoretical calculation was carried out. The conjecture was verified to a certain extent through the comparison of the theoretical calculation of XRD with the experimental results. According to the calculation results, it was found that the XRD patterns of C12A7 and its derivatives changed regularly with the change in the occupation number in the crystal cage. Under the condition that the types of vacancy atoms remained unchanged, the more vacancy atoms occupied in C12A7 crystal, the higher the peak at 2θ = 33.35° in the diffraction pattern. It was also found that the higher the atomic number of vacancy atoms in C12A7 crystal, the higher the peak at 2θ = 33.35° in the diffraction pattern. The carbon occupation number of samples at different experimental temperatures was deduced. The results showed that the carbon occupancy of the samples prepared at 990, 1,353 and 1,680°C were 11, 4 and 8, respectively.

Keywords: C12A7 derivative; X-ray diffraction; carbon occupation

1 Introduction

Mayenite (C12A7) is known as a superior electrical insulator and a type of nanoporous inorganic oxide, its unique crystal structure has attracted many researchers. Its unit cell is composed of two parts, [Ca24Al28O64]4+ + 2O2−. The first part is a positively charged lattice frame with 12 cages. The inner diameter of each cage is 0.4 nm. The second part consists of two oxygen ions. The O2− occupies two of the cages to compensate for the positive charge of the cage frame. The two oxygen ions O2− in C12A7 crystal cages can be replaced by other anions to prepare C12A7 derivatives, such as e− [1], NH2− [2], OH− [3], H− [4] or O− [5]. Many kinds of C12A7 derivatives have unique properties. C12A7: H− can be converted between insulator and conductor [6], C12A7: e− is a kind of insulator/metal transition material [7] and can be used as good conducting material [8]. There are many studies on application of C12A7 and its derivatives, such as chemical storage of ammonia [9], thermal electron/anion emission [10], catalytic steam reforming of bio oil to hydrogen [11], etc.

Kim et al. [12] removed free oxygen ions in C12A7 by external electric field, and then doped electrons into C12A7 to obtain C12A7: e−. Hayashi et al. [13] proved that NH2− can be incorporated into C12A7 crystal through ammonia heat treatment to form C12A7: NH2−. They verified that the embedded NH2 − ions were chemically stable in environmental conditions and organic solvents. It will be resolved to NH3 under vacuum conditions at temperature higher than 500°C. Therefore, it was expected that C12A7: NH2 − can be used as an active nitrogen source for in situ cage degradation nitrogen transfer reaction. In the study by Hayashi et al. [14], it was found that C12A7 crystal has high conductivity when balanced in hydrogen atmosphere above 800°C and maintains high conductivity when quenched below 600°C. Its complex conductivity behavior was related to the combination of H− in lattice skeleton cage. The results of electromotive force measurement showed that the main carrier of conductivity is electrons, and the contribution of protons (H+) was very small, which eliminates the possibility of direct migration of hydride ions. Through the combination of observation and ab initio calculation, it was concluded that electrons were thermally decomposed from hydride ions into two electrons and protons, which were further transformed into OH− ions by reacting with oxide ions (O2−) in external electric field. Hosono et al. [15] found that the free O2− in C12A7 can be replaced by various oxygen related species such as OH− and O− with different atmospheres by thermal treatment. The experimental results showed that O− is more mobile in C12A7 than O2−. Wang et al. [16] studied the hydrogen production process of catalytic steam reforming of bio oil prepared by rapid pyrolysis of biomass by using a new metal doped catalyst [Ca24Al28O64]4+ · 4O−/M (C12A7−O−/M, M = Mg, K, Ce). In the study by Kim and Hosono [17], C12A7: e− was prepared in a semi closed graphite crucible. The C12A7 powder was melted twice in a semi airtight carbon crucible. The carbon cap temperature in the crucible was 1,600°C. Meanwhile, a strong reducing atmosphere (PO2 = ∼10−16 atm) was generated in the crucible. They found that the first melting was a mixture of C3A and CA by X-ray diffraction (XRD) analysis. The formation and disappearance of C2 2− was found through Raman spectra of the products. This explained why there was no carbon residue in their product and finally obtained C12A7: e−.

In the experimental study by Yang et al. [18], it was found that carbon doping into C12A7 crystal would form a conductor. The experimental study of its electrical characteristics and thermal electron emission characteristics showed that the resistance is about 3 Ωm at normal temperature, which was similar to that of semiconductors. Its electron concentration was about 1.0 × 1018 cm3. Meanwhile, the research results of its emission performance showed that its surface work function is about 3.7 eV. It is relatively stable in the test, with a floating value of about 0.03 eV. Therefore, it has great application prospects in optoelectronic devices.

In this study, we prepared samples of C12A7 derivatives by high temperature sintering method in a sealed graphite crucible. A series of samples were prepared in different reacting temperatures. The XRD analysis of the sample proved that the final products were C12A7: C. Through simulation calculation of the theoretical model of C12A7 derivatives, we obtained the number of carbon occupying C12A7: C crystal cages in the samples.

2 Experiment

High temperature sintering method is a common method for preparing C12A7 in the laboratory. In this experiment, thermal arc is used as heating source. The arc produces high temperature and high energy electrons. The high energy electrons impact the graphite surface of the crucible then excite the carbon atom into gas. The gaseous free carbon atoms form a reducing atmosphere of C12A7 reaction.

2.1 Experimental conditions

The reagents used to prepare the reaction in the experiment include calcium carbonate powder with a purity of 99.9%, alumina powder with a purity of 99.9% and distilled water. In this experiment, calcium carbonate and alumina powder were mixed and stirred in distilled water according to the mass ratio of 1:0.595. The prepared slurry was brushed on the surface of molybdenum sheet which was then sealed in a high-purity graphite crucible and heated at high temperature to convert the slurry to C12A7.

The experimental setup is shown in Figure 1.

Figure 1 (a) The experimental device consisting of (1) tungsten electrode (+), (2) thermocouple, (3) tungsten electrode (−), (4) insulation layer, (5) insulating sealing sleeve, (6) graphite crucible, (7) high temperature arc, (8) graphite partition plate and (9) sample. (b) Graphite crucible.
Figure 1

(a) The experimental device consisting of (1) tungsten electrode (+), (2) thermocouple, (3) tungsten electrode (−), (4) insulation layer, (5) insulating sealing sleeve, (6) graphite crucible, (7) high temperature arc, (8) graphite partition plate and (9) sample. (b) Graphite crucible.

In the experiment, the sealed graphite crucible containing the sample was placed in the thermal insulation material. The inside of the crucible was heated by a high-voltage arc. The crucible temperature was monitored using the tungsten rhenium thermocouples. The arc power was adjusted by the voltage of the power supply. Then, the internal temperature of the graphite crucible could be controlled. The crucible was heated to a high temperature and the temperature was kept for several hours. After heating, the thermal insulation layer was opened to cool the device so that the temperature slowly reduced to room temperature.

2.2 XRD results of experimental samples

The sample surface photos at experimental temperature are shown in Figure 2.

Figure 2 Surface photos of samples at various temperatures: (a) 990°C, (b) 1,150°C, (c) 1,353°C and (d) 1,680°C.
Figure 2

Surface photos of samples at various temperatures: (a) 990°C, (b) 1,150°C, (c) 1,353°C and (d) 1,680°C.

In Figure 2, the surfaces of samples appear to be dark green glass texture. The distribution of the sample is nonuniform. The coatings are thick at the center of samples and thin at the edge.

The XRD patterns of the samples at various temperatures are shown in Figure 3.

Figure 3 XRD patterns of samples at various reacting temperatures: (a) sample obtained at 990°C, (b) sample obtained at 1,150°C, (c) sample obtained at 1,353°C and (d) sample obtained at 1,680°C. Note: (1) 2θ = 18.1° (2) 2θ = 29.8° (3) 2θ = 33.4° (4) 2θ = 36.7°.
Figure 3

XRD patterns of samples at various reacting temperatures: (a) sample obtained at 990°C, (b) sample obtained at 1,150°C, (c) sample obtained at 1,353°C and (d) sample obtained at 1,680°C. Note: (1) 2θ = 18.1° (2) 2θ = 29.8° (3) 2θ = 33.4° (4) 2θ = 36.7°.

In the XRD patterns of Figure 3, there are obvious main peaks at 2θ = 18.1, 29.8, 33.4 and 36.7°. Serval differences appear in the main peaks under various experimental conditions. In Figure 3a, the maximum peak is at 2θ = 18.1° and the second peak is at 2θ = 33.4°. In Figure 3b, the peak at 2θ = 36.7° is the maximum while the second peak is at 2θ = 18.1°. In Figure 3c, the maximum peak is at 2θ = 18.1° and the second peak is at 2θ = 33.4°. It is the same as Figure 3a. In Figure 3d, the maximum peak is at 2θ = 18.1°, the second peak is at 2θ = 36.7°.

The main crystal phase obtained by Jade matching is C12A7. The standard card is shown in Figure 4.

Figure 4 Standard card of C12A7.
Figure 4

Standard card of C12A7.

In Figure 4, the diffraction angle corresponding to the main peak of the XRD standard card of C12A7 is 2θ = 18.1, 29.8, 33.4 and 36.7° respectively, which are consistent with the experimental results (Figure 3a–d). Therefore, it can be preliminarily judged that the main products of the experiment are similar or consistent with the crystal structure of C12A7. Meanwhile, it can be seen that the main XRD peak intensity of the experimental product is different from that of the C12A7 standard card. It can be preliminarily determined that the main product is a derivative of C12A7. In consideration of the high temperature and hypoxia atmosphere in the graphite crucible under the experimental conditions, it was most likely that the free carbon ions dissolved into the C12A7 crystal structure and occupied the vacancy. Therefore, it can be predicted that the main product of the experiment is the carbon derivative of C12A7.

The lattice size of the sample can be calculated using the following expression [19]:

(1) D = K λ / β cos θ ,

where D is the lattice size, β is the full width at half height (FWHM), θ is the Bragg diffraction angle (°), λ is the XRD wavelength (Cu, Kα = 0.154 nm) and K is the Scheler constant (0.89). The average lattice size of each sample calculated by equation (1) is shown in Table 1.

Table 1

Lattice size of samples at different temperatures

T/°C 990 1,150 1,353 1,680
D/nm 0.883 1.178 0.914 0.965

The standard lattice size of C12A7 theoretical model is 1.198 nm. The lattice size of the sample obtained in the experiment is similar to 1.198 nm. It verifies the reliability of the conclusion that the main product of the experiment is C12A7 and its derivatives.

3 Results and discussion

The above XRD analysis shows that the sample experiment prepared maintains the crystal structure of C12A7, but is different from the standard C12A7. It is not a mixture of C3A and CA, but a C12A7 derivative. In this section, the theoretical research of crystal model is carried out. The crystal structural characteristics of C12A7 derivatives can be obtained by using crystal diffraction inversion algorithm and simulation method.

3.1 Crystal structure model and vacancy coordinates

The C12A7 cell can be regarded as a network of positively charged cages and O2− occupying two vacancies in 12 cages (Figure 5). Each cage structure has about 4 Å internal free space. Each cage is composed of 6 calcium ions, 8 aluminum ions and 16 oxygen ions. The distance between the cage centers is about 10 Å.

Figure 5 (Continued)
Figure 5 (Continued)
Figure 5

(Continued)

Sushko et al. [20] discussed the influence and properties of electrons in the cage structure. This study discusses the possibility and influence of the internal vacancy of the cage structure occupied by C in C12A7 crystal prepared in the anoxic environment by a sealed graphite crucible.

The fractional coordinates of all vacancies in C12A7 crystal (including the vacancies occupied by two free oxygen ions O2−) are shown in Table 2 [17].

Table 2

Vacancy distribution coordinates of C12A7 crystal

No. u v w
1 (O2−) −0.0064064014252 0.1546029640671 0.3523325067474
2 (O2−) −0.4294148236021 −0.2596094238932 −0.1852599479154
3 0.3642615104100 −0.0151589380301 0.2099217288235
4 −0.1387628070831 0.4856418610275 −0.2922960519320
5 0.2370313540956 0.3607933036765 −0.0419691585224
6 −0.2618163182740 −0.1394221464544 0.4559881520493
7 0.2358914657313 −0.3861164923522 0.4652731450350
8 −0.2631261451437 0.1091144403454 −0.0416837929987
9 0.4886718544147 0.2372038332323 −0.4171834659615
10 −0.0115874088355 −0.2663490700638 0.0831062765391
11 −0.3831445074550 0.4855417139526 0.2041986514129
12 0.1132598058530 −0.0151751259503 −0.2924162786590

3.2 XRD theoretical analysis of different occupations in C12A7 cages

The effects of occupation on XRD intensity can be considered from these three aspects, the kinds of atoms, number of atoms and atom occupying position. The theoretical calculation will focus on these three parameters, respectively. The basic equations of XRD are provided before theoretical calculation.

3.2.1 Calculation method of XRD intensity

For the calculation of XRD intensity of crystal, first, the mutual interference of electromagnetic waves scattered by electrons in each atom is calculated. The result is often expressed by atomic scattering factor. Then, the mutual interference between the scattered waves of atoms in a primitive cell is calculated. The total scattered wave of a protocell can be expressed by geometric structure factor. Finally, the interference between the scattered waves of each primitive cell is calculated.

The mutual interference enhancement condition between the scattered waves of each primitive cell is the interference enhancement condition between the waves scattered by each lattice point in Bravais lattice. They are determined by Laue equation or Bragg’s condition of reflection.

Diffraction direction, i.e., θ, can be described by Bragg’s equation 2dsin θ = λ, where λ states certain circumstances and θ depends on the crystal plane spacing D. The diffraction direction reflects the size and shape information of the crystal cell.

XRD basic equations are as follows. Electron scattering intensity

(2) I e = I 0 r e R 2 1 + cos 2 2 θ 2 .

Atomic scattering intensity

(3) I a = f 2 I e .

Cell scattering intensity

(4) I b = ∣ F H L K ∣ 2 ⋅ I e .

Diffraction intensity

(5) I = I 0 λ 3 32 π R e 2 m c 2 V V c 2 P ∣ F H K L ∣ 2 φ ( θ ) A ( θ ) e − 2 M ,

where I 0 is the incident X-ray intensity, λ is the incident X-ray wavelength, R is the observation distance from the sample, f is the volume of crystal irradiated, V c is the unit cell volume, P is the multiplicity factor, |F HKL | is the cell diffraction intensity (structure factor), A(θ) is the absorption factor, ψ(θ) is the angle factor and e −2M is the temperature factor.

If only the relative strength is calculated, the formula can be simplified as follows:

(6) I relative = P ∣ F H K L ∣ 2 1 + cos 2 2 θ sin 2 θ cos θ e − 2 M ,

where P is the multiplicity factor. For C12A7 crystal structure, there is no equivalent crystal plane, so P = 1.

|F HKL | is the structural factor, and the calculation formula is as follows:

(7) ∣ F H K L ∣ 2 = ∑ j = 1 n f j cos 2 π ( H u j + K v j + L w j ) 2 + ∑ j = 1 n f j sin 2 π ( H u j + K v j + L w j ) 2 ,

where the atomic scattering factor |F HKL | depends on θ, element types and λ. The scattering factors of different atoms can be calculated by Jiang Jian-sheng’s fitting formula [21].

3.2.2 XRD theoretical calculation of C12A7 derivatives

3.2.2.1 Calculation details

According to the crystal parameters of C12A7, the diffraction angles of C12A7 cell can be obtained. The diffraction angle corresponding to the peak value was calculated by XRD theory of C12A7. The structural factors corresponding to different diffraction angles of C12A7 and its derivatives could be obtained by bringing the coordinates of each atom in C12A7 ionic derivatives and the crystal plane parameters corresponding to different diffraction angles into equation (7). According to equation (6), the diffraction intensity is directly proportional to the square of the structure factor. Therefore, the relative intensity of each diffraction peak can be obtained through the structure factor.

The theoretical model of C12A7 carbon derivative is arranged according to different carbon occupation, as shown in Figure 5.

In Figure 5, green particles represent Ca, pink particles represent Al, red particles represent O, gray particles represent vacant C and are specially marked. The number after C represents the serial number corresponding to C in Table 2, and its fractional coordinates can be obtained from Table 2.

3.2.2.2 Initial calculation

The diffraction angles of C12A7 cell can be calculated by Bragg equation 2dsin θ = λ, where interplanar spacing d = 12 Å and the X-ray wavelength λ = 0.154 nm. Then the crystal face indices corresponding to the diffraction angles can be calculated by MDI Jade. The results are shown in Table 3.

Table 3

C12A7 crystal diffraction angle of plane parameters

2θ H K L
18.126 2 1 1
20.934 2 2 0
23.453 3 1 0
27.822 3 2 1
29.776 4 0 0
33.407 4 2 0
35.079 3 3 2
36.696 4 2 2
38.268 5 1 0
41.206 5 2 1
44.05 5 3 0
46.661 6 1 1
49.211 5 4 1
51.688 6 3 1
52.878 4 4 4
54.058 7 1 0
55.222 6 4 0
56.402 7 2 1
57.518 6 4 2
60.808 6 5 1
61.889 8 0 0
62.963 7 4 1
67.141 7 5 0
69.229 7 5 2
70.176 8 4 0
72.222 8 4 2
73.195 7 6 1
74.198 6 6 4
75.162 9 3 0
77.101 9 3 2
79.077 9 4 1
81.924 10 2 0
84.739 10 3 1
87.688 10 4 0
89.513 10 4 2
90.459 11 1 0

The coordinates (u, v, w) of each atom in C12A7 and its derivatives in Table 2 and the crystal plane parameters (H, K, L) corresponding to different diffraction angles in Table 3 are introduced to equation (7). The structure factor |F HKL | corresponding to different diffraction angles of C12A7 and its derivatives could be derived. The results are shown in Table 4.

Table 4

Structural factors |F HKL | of C12A7 in different cages

2θ 18.126° 29.776° 33.407° 35.079°
C12A7: 2O 38676.43 153,921 150675.1 18839.95
C12A7:1C 39263.54 154730.6 151568.9 19234.12
C12A7: 2C 38938.12 153186.3 150519.4 18697.3
C12A7: 3C 37172.7 148537.6 155200.4 18409.24
C12A7: 4C 35409.11 143948.7 159963.8 18305.94
C12A7: 5C 33193.01 148537 159890.9 16721.61
C12A7: 6C 31048.86 153193.2 159764 15208.5
C12A7: 7C 31142.18 157925.6 159813.8 14954.94
C12A7: 8C 31436.8 162730 159766.6 15005.61
C12A7: 9C 29359.74 167599.1 164583.1 16052.75
C12A7: 10C 27361.16 172541.8 169485.2 17242.1
C12A7: 11C 25836.07 167638.6 174413.7 15704.69
C12A7: 12C 24348.75 162766.7 179457.7 14243.71
2θ 36.696° 41.206° 46.661° 55.222° 57.518°
C12A7: 2O 107766.2 46299.73 26158.08 219031.5 142282.1
C12A7:1C 109061.9 45772.37 25665.4 220899 142115.4
C12A7: 2C 107860.5 46215.64 26183.49 221370.8 143627.1
C12A7: 3C 111416.9 45586.01 24283.7 221254.9 144034.2
C12A7: 4C 114863.6 44785.22 22451.32 221740.5 143959.5
C12A7: 5C 112890.4 42602.91 23745.72 227417.5 148546.6
C12A7: 6C 110991.2 40518.58 25149.12 233175 153203.7
C12A7: 7C 112525.7 38542.73 23929.8 239004 157881.1
C12A7: 8C 114573.8 36546.8 22730.88 244873.9 162684.4
C12A7: 9C 112802.7 36918.19 24245.58 250843.1 162136.9
C12A7: 10C 110932.7 37476.68 25800.01 256878.9 162121.6
C12A7: 11C 114625.4 39809.17 23995.84 257640.6 161560.4
C12A7: 12C 118292.4 42166.43 22208.16 257541.1 161605.7

3.2.3 Effect of different kinds of atoms occupying the cages of C12A7 crystal

Taking H, C and O as examples, make them occupy vacancies 1–6 in the theoretical model of C12A7 crystal in turn (coordinates of the vacancies can be seen in Table 2). The calculated diffraction patterns of [Ca24Al28O64]4+(H−)4H2, [Ca24Al28O64]4+(e−)4C6 and [Ca24Al28O64]4+(O2−)2O4 are shown in Figure 6.

Figure 6 Diffraction pattern of XRD when different atoms occupied vacancies 1–6. (a) H occupied vacancies 1–6, (b) C occupied vacancies 1–6 and (c) O occupied vacancies 1–6.
Figure 6

Diffraction pattern of XRD when different atoms occupied vacancies 1–6. (a) H occupied vacancies 1–6, (b) C occupied vacancies 1–6 and (c) O occupied vacancies 1–6.

In Figure 6, the position of the main peak in the diffraction pattern basically does not change with the kind of atoms occupying the vacancy. The maximum peak is at 2θ = 18.1°, i.e. I 1 = 1. The second peak is at 2θ = 33.35° and the relative value of the second peak is denoted as I 2. The comparative results of I 2 are I 2H < I 2C < I 2o.

According to equations (1)–(6), the parameter affected by the kind of atom is the scattering factor |F HKL | of the atom in equation (6), and then the structure factor. While θ and λ are constants, the scattering factor increases with the increment of atomic number. The atomic number of oxygen is higher than that of carbon and hydrogen. Therefore, the peak at 2θ = 33.35° increases with the increase in the atom number of atoms in C12A7 crystal vacancy. It is consistent with the diffraction pattern results of I 2H < I 2C < I 2o.

Based on this study, it can be considered that the more the atomic number of vacancy atoms in C12A7 crystal, the higher the relative diffraction intensity at 2θ = 33.35°.

3.2.4 Effect of different numbers of atoms occupying the cages of C12A7 crystal

In this experiment, it is speculated that the product should be a carbon derivative of C12A7. Therefore, the vacancy occupied by carbon is taken as an example in the calculation. Diffraction pattern of C12A7: nC (n = 1∼12) are calculated by theoretical model of C occupying the C12A7 crystal cages. The results are shown in Figure 7.

Figure 7 Diffraction pattern with different number of C occupying [Ca24Al28O64]4+(e−)4C1–12. (1) C occupies vacancy 1, (2) C occupies vacancy 1–2, (3) C occupies vacancy 1–3, (4) C occupies vacancy 1–4, (5) C occupies vacancy 1–5, (6) C occupies vacancy 1–6, (7) C occupies vacancy 1–7, (8) C occupies vacancy 1–8, (9) C occupies vacancy 1–9, (10) C occupies vacancy 1–10, (11) C occupies vacancy 1–11 and (12) C occupies vacancy 1–12.
Figure 7 Diffraction pattern with different number of C occupying [Ca24Al28O64]4+(e−)4C1–12. (1) C occupies vacancy 1, (2) C occupies vacancy 1–2, (3) C occupies vacancy 1–3, (4) C occupies vacancy 1–4, (5) C occupies vacancy 1–5, (6) C occupies vacancy 1–6, (7) C occupies vacancy 1–7, (8) C occupies vacancy 1–8, (9) C occupies vacancy 1–9, (10) C occupies vacancy 1–10, (11) C occupies vacancy 1–11 and (12) C occupies vacancy 1–12.
Figure 7

Diffraction pattern with different number of C occupying [Ca24Al28O64]4+(e−)4C1–12. (1) C occupies vacancy 1, (2) C occupies vacancy 1–2, (3) C occupies vacancy 1–3, (4) C occupies vacancy 1–4, (5) C occupies vacancy 1–5, (6) C occupies vacancy 1–6, (7) C occupies vacancy 1–7, (8) C occupies vacancy 1–8, (9) C occupies vacancy 1–9, (10) C occupies vacancy 1–10, (11) C occupies vacancy 1–11 and (12) C occupies vacancy 1–12.

In Figure 7, the position of the maximum peak in the diffraction pattern basically does not change with the number of vacant carbon atoms. The relative intensities of the corresponding peaks are at 2θ = 18.1°, i.e., I 1 = 1. The second peak is at 2θ = 33.35°. The relative value of the second peak (I 2) increases with the increment of the number of carbon atoms.

From the point of view of the calculation formula, the main parameter affected by the occupation of vacancies in C12A7 crystal from equations (1)–(6) is the structure coefficient |F HKL |2 in equation (5). It can also be seen from the calculated structure factor Table 3 that with the increase in the number of vacancy atoms in the C12A7 crystal structure, the overall trend of the structure factor value at 2θ = 18.1° decreases gradually. The absolute diffraction intensity decreases correspondingly. The relative diffraction at 2θ = 33.35° is the ratio of absolute diffraction at 2θ = 33.35° to absolute diffraction at 2θ = 18.1°. Therefore, the relative diffraction intensity at 2θ = 33.35° increases with the increase in the number of occupied atoms, which is consistent with the results of the diffraction pattern.

In the diffraction pattern of C12A7: C theoretical model with various carbon occupation, I 2 (2θ = 33.35°) is shown in Figure 8.

Figure 8 Variation curve of relative intensity of diffraction peak at 2θ = 33.35° with carbon occupation number.
Figure 8

Variation curve of relative intensity of diffraction peak at 2θ = 33.35° with carbon occupation number.

The peak value I 2 increases with the increase in carbon occupation. The more the occupation, the more obvious the increasing trend. The influence of the diffraction pattern of the occupancy C12A7 derivative is that the more the number of atoms occupying the vacancy in the C12A7 crystal, the higher the I 2 in the diffraction pattern.

3.2.5 Different atom occupying position effect in C12A7 crystal cages

Taking the carbon occupation number 4 as example, the calculated diffraction patterns of [Ca24Al28O64]4+(e−)4C4 occupying different vacancy positions are shown in Figure 9.

Figure 9 Diffraction pattern with C occupying different positions in [Ca24Al28O64]4+(e−)4C4. (a) C occupies vacancies 1–4, (b) C occupies vacancies 5–8 and (c) C occupies vacancies 9–12.
Figure 9

Diffraction pattern with C occupying different positions in [Ca24Al28O64]4+(e−)4C4. (a) C occupies vacancies 1–4, (b) C occupies vacancies 5–8 and (c) C occupies vacancies 9–12.

It can be seen from Figure 9 that the occupied vacancy position has little effect on the diffraction pattern. It is much less than that of atomic number and occupation number. Therefore, the influencing factors of occupying vacant positions is not important for further analysis.

3.3 Determination and analysis of prepared crystal structure

3.3.1 Experimental phenomena and analysis

The XRD results of the experimental samples show that the diffraction angle corresponding to the maximum diffraction peak is basically the same as that of C12A7, but the relative peak is obviously different. Based on calculation results, if the vacancy oxygen ion of C12A7 is replaced or other vacancy of the crystal cage is occupied, the position (diffraction angle) of each diffraction peak changes very little. The peak (relative diffraction intensity) will change significantly with the variety and quantity of vacancy ions. Therefore, it can be inferred that the experimental product is a C12A7 derivative.

At the same time, considering that the experimental condition is a sealed graphite crucible, the interior of the crucible is a sealed strong reduction atmosphere, and the oxygen will be completely converted into CO, so the possibility of oxygen occupying C12A7 vacancy can be roughly ruled out. Because the samples are heated by thermal arc in the graphite crucible, the arc temperature is much higher than the surface temperature of the sample. At this temperature, it is possible to melt the graphite at high temperature and produce activated carbon ions. The carbon can replace the free oxygen ions in the C12A7 cage structure and occupy other vacancies in the cage structure. The new carbon derivatives of C12A7 could be reformed.

The crucible inner reaction process is speculated as follows:

At 500–850°C:

2 C + O 2 → 2 CO CaCO 3 → CaO + CO 2 C + CO 2 → 2 CO

Inside the crucible, graphite can be oxidized at 500°C to produce CO. At about 825°C, the calcium carbonate on the sample surface decomposes into calcium oxide and carbon dioxide. At above 777°C, graphite further reacts with carbon dioxide to form carbon monoxide, thus forming a reducing atmosphere inside the crucible.

Above 1,000°C:

24 CaO + 14 Al 2 O 3 → [ Ca 24 Al 28 O 64 ] 4 + + 2 O 2 − ( cage ) [ Ca 24 Al 28 O 64 ] 4 + + 2 O 2 − ( cage ) + 4 C → Ca 24 Al 28 O 64 C 2 + 2CO Ca 24 Al 28 O 64 C 2 + n C → Ca 24 Al 28 O 64 C n +2

At more than 1,000°C, calcium oxide reacts with aluminum oxide to produce calcium aluminate. At the same time, due to the high temperature arc heating used in this experiment, the arc center local can reach a very high temperature. The graphite will melt or excite to produce free carbon. The free carbon will first replace the oxygen in the cage vacancy of calcium aluminate crystal to reform carbon derivatives. Subsequently, it will further occupy other vacancies in the crystal cage to reform derivatives with different carbon content.

3.3.2 Analysis of C occupation in experimental samples

Through further analysis of the experimental data, the fine structure of carbon occupation in the cage of C12A7 derivative can be determined. The calculation of diffraction intensity I 1 and I 2 corresponding to different carbon occupation ratios are shown in Table 5.

Table 5

Ratio of I 1 and I 2 corresponding to different carbon occupation numbers

Occupancy I 1 (2θ = 18.1°)/% I 2 (2θ = 33.35°)/%
0 100 50.03181
1 100 51.52849
2 100 52.9908
3 100 56.09875
4 100 59.35438
5 100 62.95118
6 100 66.71947
7 100 70.83137
8 100 75.16638
9 100 79.68706
10 100 84.41227
11 100 90.08013
12 100 96.0659

The ratio of I 1 to I 2 corresponding to different experimental temperature conditions is shown in Table 6.

Table 6

Ratio of I 1 and I 2 corresponding to the experimental temperature conditions

T I 1 (2θ = 18.1°) I 2 (2θ = 33.4°) I 2/I 1
990°C 1,006 931 92.54473
1,150°C 14,378 1,489 10.3561
1,353°C 3,066 1,832 59.75212
1,680°C 1,674 1,251 74.73118

According to the comparison of the above data in Tables 5 and 6, it can be estimated that the carbon occupation number of the samples prepared at 990, 1,353 and 1,680°C is 11, 4 and 8, respectively. The sample at 1,150°C does not match the calculated results. It may be due to the failure to clean up the graphite adhered to the sample surface after melting, resulting in the error of the experimental results. It is difficult to control the experiment under high temperature conditions. The repeatability of sample preparation needs to be improved.

4 Conclusion

A series of samples of C12A7 derivative were prepared by high temperature sintering in a sealed graphite crucible. XRD analysis shows that the crystal diffraction pattern of the sample is basically consistent with the C12A7 standard card in the position of the maximum peak, but there are differences in the relative intensity of each maximum peak. Because the preparation reaction of this experiment adopts high-temperature arc heating in a sealed graphite crucible, it is speculated that this difference is likely caused by the presence of carbon occupation in the crystal according to the experimental conditions. In order to verify this conjecture, the theoretical model of C12A7 derivatives with different carbon occupation numbers was established, and the XRD theoretical calculation was carried out. Through the comparison of the theoretical calculation of XRD with the experimental results, the experimental samples were determined as C12A7: C. According to the calculation results, it was found that the XRD patterns of C12A7 and its derivatives changed regularly with the change in the occupation number in the crystal cage. Under the condition that the kinds of vacancy atoms remained unchanged, the more the number of vacancy atoms occupied C12A7 crystal, the higher the peak at 2θ = 33.35° (I 2) in the diffraction patterns. At the same time, it was also found that the more the atomic number of vacancy atoms in C12A7 crystal is, the higher the peak at 2θ = 33.35° in the diffraction pattern. The carbon occupation number of samples at different experimental temperatures was deduced. The results showed that the carbon occupancy of the samples prepared at 990, 1,353 and 1,680°C were 11, 4 and 8, respectively. There was a good agreement between the theoretical and experimental results. It proved that the sample structure speculated in this study is reliable to a certain extent.

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Conflict of interest: The authors declare no conflicts of interest regarding this article.

  3. Data availability statement: The data that support the findings of this study are available from the corresponding author, Cong Ji, upon reasonable request.

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Received: 2022-11-01
Revised: 2023-03-06
Accepted: 2023-03-28
Published Online: 2023-06-26

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/secm-2022-0197
Keywords for this article
C12A7 derivative; X-ray diffraction; carbon occupation
Creative Commons
BY 4.0

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